Airline trade groups filed suit on Friday to prevent the Federal Aviation Administration from furloughing air-traffic controllers, a step the FAA has warned could cause thousands of daily flight delays beginning this weekend.

Industry trade group Airlines for America said it filed a motion in the U.S. Appellate Court for the District of Columbia, seeking a stay to halt the FAA's plan to meet a portion of its budget reduction under the sequester by requiring controllers to take one day off without pay for every 10 work...